The total number of four-digit numbers such that each of the first three digits is divisible by the last digit is equal to:

How many $5$-digit numbers can be formed using the digits $0, 1, 2, 3, 4,$ and $5$ without repetition such that the number is divisible by $3$?

$3$ boys $B_i, i = 1, 2, 3$ and $6$ girls $G_i, i = 1, 2, . . . , 6$ are to be seated in a row. The number of ways they can be seated so that $B_1, B_2$ are separated and $G_1, G_2$ are also separated is equal to:

The total number of $5$-digit telephone numbers that can be formed such that at least one digit is repeated is .... (The first digit cannot be $0$).

The number of different words that can be formed using all the letters of the word $APPLICATION$ such that no two vowels come together is -

$A$ test containing $3$ objective-type questions is conducted in a class. Each question has $4$ options and only one option is the correct answer. No two students of the class have answered identically,and no student has written all correct answers. If every student has attempted all the questions,then the maximum possible number of students who have written the test is: